I have a dataset where the features are skewed (non normal) distributions. My preprocessing pipeline consists of the following steps:
- Missing values imputation
- Centering and scaling (zero mean and unit variance) of each feature
- Transforming the features to an approximate normal distribution by using the Box-Cox Transformation.
Should I first do the centering and scaling or the transformation?
Second, if the distributions are skewed (not normal) is centering and scaling (zero mean and unit variance) still ok? Another possiblity would be to subtract the median (instead of the mean) and dividing by 1.5 * the interquartile range (instead of the standard deviation).